The invention concerns a method of obtaining a spectrum in an optical Fourier transform (FT) spectrometer with an interferometer and a detector for recording optical signals from the interferometer and converting into electrical signals, and also, if necessary, further signal processing elements, wherein an interferogram in an interesting wave length range (=effective interferogram) and a reference interferogram in a narrow-band reference wave length range are recorded simultaneously or with fixed phase shift, wherein the effective interferogram is digitized in a time-equidistant manner and wherein a digital compensation filter is applied to the sampled effective signals which compensates the complex frequency response consisting of the amplitude and phase responses of the detector and of all further signal processing elements.
A method of this type is known from the article titled "New approach to high-precision Fourier transform spectrometer design" by J. W. Brault in the journal Appl. Optics, Vol. 35, No. 16, pages 2891-2896, Jun. 1, 1996.
Optical spectroscopy, in particular infrared Fourier transform (IR-FT) spectroscopy is one of the most effective tools available to the analytical chemist in research, application and process control. Common methods of recording such optical spectra are described in all details e.g. in a series of articles by J. Gronholz and W. Herres with the title "Datenverarbeitung in der FT-IR-Spectroskopie" (data processing in FT-IR spectroscopy) in the journal Comp.Anw.Lab., Edition 5/1984, pages 352-356, Edition 6/1984, pages 418-425 and Edition 5/1985, pages 230-240. In this connection, zero crossings of a reference interferogram, which is recorded e.g. by an HeNe laser, are measured in their temporal sequence and the simultaneously recorded effective interferogram is digitized at these zero positions.
The hitherto common method, applied in optical FT spectrometers from the infrared to the ultraviolet range, of sampling the detector signal at equal intervals of optical path difference with reference to the position of the interferometer mirror (in a Michelson interferometer), however, does not allow exact compensation of the amplitude and phase responses of the detector, since the actual speed of the interferometer mirror is not known. For this reason, it is not possible to compensate differences and distortions of the transit time between effective signal and reference signal due to an apparatus function. Any speed variation of the mirror drive will therefore cause side band modulation in the spectral lines. For this reason, operational methods for spectrometers of this type are not suited for systems with heavy mechanical disturbances, e.g. in the vicinity of vibration generating machines or for spectrometers which are mounted e.g. on movable vehicles.
The initially cited publication by J. W. Brault describes, in contrast thereto, a method of compensating the amplitude and phase responses which can be used with particular efficiency in a system with time-equidistant sampling of the optical signal. By means of "pre"digitization of the effective signal with fixed time periods by means of an analog-to-digital converter (ADC), the apparatus function of the detector and the further signal processing elements can essentially be removed from the spectra by deconvolution. In the following, the method according to J. W. Brault is described in detail:
The time-equidistant sampling enables determination of the development with time of the detector signal. A digital filter (called compensation filter) can be applied to said sampled signal, which filter comprises the reciprocal complex frequency response (consisting of amplitude and phase responses) of the detector and the further signal processing elements. At the output of this filter, values are obtained which correspond to the optical signal at the input of the detector multiplied by its spectral responsivity delayed merely by a constant time period. The signal is independent of the driving speed of the interferometer mirror.
In order to obtain from the detector signal an interferogram which is independent of the speed variations of the movable mirror in the interferometer, spatially equidistant sampling of the IR detector signal is necessary. In order to convert the signal, which was sampled at equal time intervals, into a spatially equidistantly sampled signal, signal values are calculated by means of a digital filter with constant delay (called an interpolation filter) at those points in time, at which the optical path difference in the interferometer achieves certain values, i.e. values, at which the movable mirror/s in the interferometer is/are at certain locations.
Since the compensation filter and the interpolation filter operate in the time domain in each case, they can be applied one after the other.
Since the two filters are applied one after the other and both are time domain filters, they can be combined in one filter by convolving their filter coefficients. This reduces the requirements concerning the storage need and the speed of the digital filter processor.
Finally, a further digital filter (called spatial frequency filter) can be applied to the resulting values of the combined compensation and interpolation filter, which carries out reduction of the data to the desired spectral range. This filter cannot be linked with the combined filter since it has to be applied to spatially equidistant sampling values; however, it can be carried out by the same processor.
A particular advantage of the Brault method consists in the fact that extremely cheap ADCs from mass production in audio technology can be used. This time-equidistant sampling method enables simultaneous recording of the variations in time and the absolute positions of the zero crossings of the reference signal. After corresponding conversion of the ADC signals to spatially equidistant positions of the mirror (interpolation filter), a signal quality can be achieved which is at least equal to the one of the above-described spatially equidistant sampling method, wherein, however, the experimenter is given a considerably higher degree of flexibility since not only the zero crossings, but also any intermediate values can be employed for digitization. A further very important advantage of the Brault method is the possible correction of the apparatus function by means of the above-described compensation filter which corresponds to a deconvolution of the transfer function of the detector from the spectra.
In contrast thereto, it is the object of the present invention to provide a method on the basis of the suggestion by Brault, in which an essential component, namely the detection of the compensation filter and thus the deconvolution of the transfer function of the detector and the signal processing elements from the spectra is rendered possible in a particularly effective manner by means as simple as possible.